A Guide to First-Passage Processes

Sidney Redner

ISBN 10: 0521036917 / ISBN 13: 9780521036917

Published by Cambridge University Press, GB, 2007

About this Item

First-passage properties underlie a wide range of stochastic processes, such as diffusion-limited growth, neuron firing and the triggering of stock options. This book provides a unified presentation of first-passage processes, which highlights its interrelations with electrostatics and the resulting powerful consequences. The author begins with a presentation of fundamental theory including the connection between the occupation and first-passage probabilities of a random walk, and the connection to electrostatics and current flows in resistor networks. The consequences of this theory are then developed for simple, illustrative geometries including the finite and semi-infinite intervals, fractal networks, spherical geometries and the wedge. Various applications are presented including neuron dynamics, self-organized criticality, diffusion-limited aggregation, the dynamics of spin systems and the kinetics of diffusion-controlled reactions. First-passage processes provide an appealing way for graduate students and researchers in physics, chemistry, theoretical biology, electrical engineering, chemical engineering, operations research and finance to understand all of these systems.

Seller Inventory # LU-9780521036917

Bibliographic Details

• Title: A Guide to First-Passage Processes
• Publisher: Cambridge University Press, GB
• Publication Date: 2007
• Language: English
• ISBN 10: 0521036917
• ISBN 13: 9780521036917
• Binding: Paperback
• Condition: New
• Weight: 480 grams

About this title

Synopsis

First-passage properties underlie a wide range of stochastic processes, such as diffusion-limited growth, neuron firing, and the triggering of stock options. This book provides a unified presentation of first-passage processes, which highlights its interrelations with electrostatics and the resulting powerful consequences. The author begins with a modern presentation of fundamental theory including the connection between the occupation and first-passage probabilities of a random walk, and the connection to electrostatics and current flows in resistor networks. The consequences of this theory are then developed for simple, illustrative geometries including the finite and semi-infinite intervals, fractal networks, spherical geometries and the wedge. Various applications are presented including neuron dynamics, self-organized criticality, diffusion-limited aggregation, the dynamics of spin systems, and the kinetics of diffusion-controlled reactions. Examples discussed include neuron dynamics, self-organized criticality, kinetics of spin systems, and stochastic resonance.

About the Author

Sid Redner is a condensed-matter theorist whose research focuses on non-equilibrium statistical physics and its applications. Dr Redner has been on the physics faculty at Boston University since 1978 and has been a full professor since 1989. He has published 230 research articles and is the author of A Kinetic View of Statistical Physics with P. L. Krapivsky and E. Ben-Naim (Cambridge University Press, 2010). Dr Redner is a Fellow of the American Physical Society and was a visiting scientist at Schlumberger Research in 1984–1985, the Ulam Scholar at Los Alamos National Laboratory in 2004–2005 and a visiting professor at the Universite Paul Sabatier (Toulouse) and Universite Pierre et Marie Curie (Paris) in 2008.